Combinatorics and algebra of tensor calculus
Abstract
In this paper, motivated by the theory of operads and PROPs we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2015
- DOI:
- 10.48550/arXiv.1501.01790
- arXiv:
- arXiv:1501.01790
- Bibcode:
- 2015arXiv150101790H
- Keywords:
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- Mathematics - Category Theory
- E-Print:
- 88 pages